Random Gaussian cubic surface Seed: 57 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0919 x*z^2 +0.128 y*z^2 +0.432 z^2 +0.369 x^2*z +0.0438 x*y*z +0.101 x*z -0.328 y^2*z -0.109 y*z +0.0887 z +0.217 x^3 -0.224 x^2*y -0.229 x^2 +0.143 x*y^2 +0.204 x*y -0.302 x +0.0912 y^3 +0.372 y^2 +0.00464 y +0.25 1
Affine cubic: f(x,y,z) = 0.0919 x*z^2 +0.128 y*z^2 +0.432 z^2 +0.369 x^2*z +0.0438 x*y*z +0.101 x*z -0.328 y^2*z -0.109 y*z +0.0887 z +0.217 x^3 -0.224 x^2*y -0.229 x^2 +0.143 x*y^2 +0.204 x*y -0.302 x +0.0912 y^3 +0.372 y^2 +0.00464 y +0.25 1
Shadow: the quartic B(x,y)^2 - 4 A(x,y) C(x,y) = 0 is drawn on the z=-4 xy-plane in the same 3D scene. The translucent ruled curtain rises upward from the shadow to the ramification curve where the lifted point has z >= -2 and lies above the displayed projection plane. The 3 real projected lines on the xy-plane are bitangents found from the projective lines on the cubic surface. Same-color transparent line projection cones are included but hidden by default; use the page toggle to show them.
Viewing box: axis ranges are [-4, 4].